xviii NOTATIONS

/', D/ derivative (as a function): 8.1

/'(a), D+/(a) derivative on the right: 8.4

/;03), D_/(j8) derivative on the left : 8.4

integral: 8.7

, exp(x), log x (x real) : 8.8

i/(0i, #2)5 D2/(tfi, a2) partial derivatives: 8.9

derivatives: 8.10

=«

/"(*0), D2/(*0),/(»(*0), D*/(x0) higher derivatives: 8.12

/* p regularization: 8.12, prob. 2

<^P)(A) space ofp times continuously differentiate mappings :

8.13.

|a|, Ma, Da, DMa (a composite index): 8.13

ez, exp(z) (z complex): 9.5

sin z, cos z sine and cosine: 9.5

7i 9.5

logz, am(z), I I, (1 + zf (z, t complex numbers): 9.5, prob. 8

7° opposite path: 9.6

yl v y2 juxtaposition of paths: 9.6

/(z) dz integral along a road: 9.6

j(a; y) index with respect to a circuit: 9.8

E(z,p) primary factor: 9.12, prob. 1

.T(z) gamma function: 9.12, prob. 2

y Euler's constant: 9.12, prob. 2

/(z) dz integral along an endless road: 9.12, prob. 3

o)(a;/), co(a) order of a function at a point: 9.15

JS?(E) algebra of operators : 1 1 . 1

uv composed operator: 11.1

sp(w) spectrum: 11.1

E(Q, E(C ; u) eigenspace : 1 1 . 1

u continuous extension: 11.2

N(A), N(A; w), F(/l), F(A; w) subspaces attached to an eigenvalue of a com-

pact operator: 11.4

k(X), k(l; u) order of an eigenvalue: 11.4

u* adjoint operator : 1 1 .5

I

I space of absolutely convergent series: 5.7, prob. 1